Sure it can. Let the "direction" be some angle &theta; measured from some ray about some origin. This direction can be quantized if, for instance, &theta;=n&theta;0+&phi;.

A physical example of "quantization of direction" is found in a hydrogen atom. Take the l=1 state. Its magnetic substates have the quantum numbers ml=-1,0,1. Listing them out with their eigenvalues, we have, for states |l,ml>,

Thanks for your inputs. I gathered from your reply that you are more of a physical group than that of a math group by your example of the hydrogen atom.

There are two known physical concepts that are still bothering me for a while now. These are (1) the flow of time and (2) the expansion of the universe.

For the first, the "direction" of time is linear (increasing entropy of thermodynamics). It has a beginning and an end point. These points imply unidirectionality. But a quantized time direction must necessarily imply bidirectionality as indicated by the worldline of the positron and the worldline of the electron.

For the second, the expansion of the universe does not have a center of expansion hence no expansion "direction." Is it possible for us to locate the center of the big bang by means of math logic?

Originally posted by Antonio Lao
For the first, the "direction" of time is linear (increasing entropy of thermodynamics). It has a beginning and an end point. These points imply unidirectionality. But a quantized time direction must necessarily imply bidirectionality as indicated by the worldline of the positron and the worldline of the electron.

I don't understand. The "direction" of time is quantized. It can (in principle) only take on the discretely defined values of "forward" and "backward".

For the second, the expansion of the universe does not have a center of expansion hence no expansion "direction."

Same thing here: The "direction" of expansion of the universe is quantized. It can go forward or backward.

Is it possible for us to locate the center of the big bang by means of math logic?

Cosmology is not my strong suit, but I believe it is the currently accepted view that the center of the big bang cannot be located, because the big bang happened everywhere.

Thanks again for your elucidations. It seems that I'm just much worrying for nothing.

But I still don't understand what is going on in the research in quantum gravity, if time (forward-backward) and space (forward-backward) are already quantized?

Note: In the book by Lee Smolin entitled "three Roads to Quantum Gravity", he defines "quantum Gravity" as the theory that unifies quantum theory with Einstein's general theory of relativity

I always get the impression that quantum gravity is about quantizing the "direction" of spacetime's worldline, when the worldline is made into a loop. Can we, mathematically speaking, make a loop from the worldline of spacetime? Can this loop still kept the meaning of past and future of time? Although the loop should be able to define a distance (Planck length's diffeomorphism?), but how this loop can increase its radius locally for the effect of global expansion of space?

Originally posted by Antonio Lao
But I still don't understand what is going on in the research in quantum gravity, if time (forward-backward) and space (forward-backward) are already quantized?

It's not the quantization of "direction" of time and space that is of concern in quantum gravity. Rather, it's the quantization of the metric. We are used to thinking of spacetime as a continuum. That is, we are used to thinking of any two points in space as having an uncountably infinite number of points between them. Loop quantum gravity starts from the assumption that the number of points between any two points is countable, as in a lattice grid.

I'm afraid I don't know enough about the subject to answer your other questions.

Would it also be fare to say that Plank’s length, quarks and electrons restrict the size of the LQG field?

If direction can be quantized, the quark and electrons are one-dimensional in the superstring theory, originally there was 10 or 11 dimensions - what form or shape have the missing 6 or 7 dimensions turned into - can we see them.

If direction can be quantized - can it be polarized in 3-D to give different flavours according to its direction and polarization at time of formation?

I am going to describe what I know about LQG and Higgs field. It's up to you to decide whether they are similar.

LQG - This theory is based on Feynman's lectures on gravitation at Caltech 1962-63. He used his widely known diagrams and perturbation theory similar to that found in QED. If there is no loops in the diagrams, the interactions can be described by the classical theory in spite of the difficulties with renormalization. Feynman only got as far as making single loop correction for quantum gravity. There are problems with infinities that cannot be taken away. Maybe there are still people working on these problems. This could still be a research in progress.

Higgs field - This scalar field is theorized to exist for explaining the masses of the W and Z quanta in the electroweak theory. The quanta of the Higgs field are the Higgs bosons (not found by experiments). The W and Z particles get their mass by swallowing the Higgs bosons. It is theorized that all massive particles get their mass by the Higgs mechanism. That is by swallowing the Higgs bosons. This is also research in progress.

My only suggestion to you is simple, remember you might be dealing with up to 10 dimensions, all of which may or may not be quantized, each may have their own unique qualities, charge, spin, mass, seconds.

As a Physicist we must observe the experiment, without becoming part of it.

Time has many definitions to many things, tree rings caused by the passage of the seasons, human achievement and life is not measured in years.....

Time is just another dimension, once we can accept that the rest is made easier.

In your initial question, you said,

“I am considering myself belonging to the physics group. So I am welcoming people from the math group to supply inputs for insights on the concept of "direction."”

“At the outset, we need to clarify (hopefully come to some sorts of agreement) the meaning of the word "direction" for two groups of people, (1) the mathematicians and (2) the physicists.”

I therefore consider myself one of the lucky one’s, for I’m a scientist.

How can we attempt to solve the GUT, if we can’t even ‘unite’ scientists.

What belongs to Mathematicians, who hold the key and it’s secretes.

The key, which was forged by the theories and discoveries made by Physicists, Chemist and Mathematicians – and yet know no one can tell you what one is?

For once I believe science should converge rather than diverge on this subject – we may already be a loop, or a superstring or part of loop quantum gravity or even already in a worm whole looking out.

Have you heard my story about the flatlander, who found the knife ‘point’?

Regards

Terry Giblin

PS

In one of the replies Tom said

"Cosmology is not my strong suit, but I believe it is the currently accepted view that the center of the big bang cannot be located, because the big bang happened everywhere."

Thanks for the warning about the spectre of the 10 dimensions. What I am trying to do is to restrict my research on only four dimensions or less and by doing this I am avoiding any dimension greater than four. Can I getaway with it? Time will tell.

You mentioned about four qualities found in any physical theory: charge, spin, mass, and time. As far as the acceptance of current physics, these are all quantized.

The concept of “direction” is implied in charge, spin, and time but not in mass. Mass is a product of the Higgs field, which by its definition has no sense of “direction.” It is a scalar field.

A few days ago, I came to realize that the rise of superstring theories is just to put “direction” into scalar fields because physicists never have any real problem with point-charges such as electrons or the quarks although the existence of a magnetic dipole moment (charge distribution) for all fermions indicate the existence of internal structure. But no experiment can detect this internal structure and I think this structure can never be detected no matter how small (smaller than Planck scale) the scale is. The smaller the scale the closer the experiments approach the singularity (the time is zero moment of the big bang). At the exact moment of the singularity, all physics is meaningless. The singularity has dimension zero. It has volume zero. It has time zero. But its energy is infinite. What I am adding is that at the singularity, it has infinite number of “direction” or degree of freedom.

The divergence of physicists and mathematicians was never more apparent than after the rise of superstring theories. The recent research in supersymmetry does not make the divergence any better or any worse. Mathematicians based their assertions on pure logic and definitions, while the physicists based theirs on empirical data. But at the singularity, both camps cannot retain their grip of reality.

FYI: GUT can only theorize about the unification of three forces (EM, weak, strong) or two forces (depending whether one consider EM and weak forces as electroweak force). GUT would like to include the force of gravity. But so far, this is still not possible using the current theories. Research in LQG, supersymmetry, and supergravity can only hope to do it. I don’t belong in this belief.

What I am trying to assert in my research is the idea that what we called the vacuum is that it is nothing but a connection, a bridge between our world and a parallel world. The experimentally verified vacuum fluctuation in the creation of virtual particles is a proof that a dynamic exists between these two parallel worlds. This dynamic is describable as the Higgs field.

I have not heard about your story of the flatlander, who found the knife ‘point’? Please tell me about it. This might hold the key to solving the Higgs field. Thanks.

I am getting my information about cosmology from the following sources:

1. The Big Bang, 3rd ed by Joseph Silk.
2. Principles of Physical Cosmology by P.J.E. Peebles.
3. Supernovae and Nucleosynthesis by David Arnett.
4. Gravitation by Misner, Thorne, Wheeler.
5. Gravitation and Inertia by Ciufolini, Wheeler.
6. The Measure of the Universe by J.D. North.
7. Gravitation and Cosmology by Steven Weinberg.
8. Classic books by Sir Arthur Eddington and Chandrasekhar
9. A Brief History of Time by Stephen W. Hawking
10. The Anthropic Cosmological Principle by Barrow and Tipler
11. Popularized Books by John D. Barrow, John Gribbins, Michio Kaku, A. Zee, Lee Smolin, Paul Davis, Brian Greene and many others.

The equation you wrote is identical to mine, how many times have you solved this equation - I've lost count.

The last time I saw this equation was at a lecture in December 2003 about that month's latest theory about Quarks.

I realised that I had seen this theory and solution many times before the first learnt about this equation from P.W. Atkins Physical Chemistry, 20 years ago when I was studying my A-levels. All Physicists and Mathematicians should own a copy of this book.

After 20 years of research, the Quark theory can still be approximated and best understood by a simple Taylor series.

Is the Quark theory taught at A-Level - it should be.

Now apply this equation, no approximations to the 6 dimension, to the YDSE, with your eyes open . P.W. Atkins Physical Chemistry page 412 Fig. 13.16

Lets assume we start with an electron of mass 1, which wants to transform itself into an photon and other particles, but lets assume the simplest solution one or two photons.

Apply conservation of everything, what goes in must come out (some where).

We started with an electron mass 1 and give it a choice of going through two doors. The electron is very clever, its heard of Quantum Mechanics, the Standard Model and the String Theory, takes a vote and decided to turn into a interference pattern to confuse everyone for fun.

Where has the mass gone, applying classical mechanics to this experiment the mass must have been transfer to the photon, which must have a mass 1 or its equivalent. - The transfer of energy and matter.

What mass are we taking about - try plotting a probability graph for the transfer of mass, an electron vs a photon, from 1 to 0 and 0 to 1 respectively applying the Taylor approximation.

Remember this is a loop a closed loop, you can join the points, they meet where the flatlander finds the knife point.

Interference patterns are only possible for radiation sources that are coherent. Photons of the same frequency or wavelength and also the waves are in phase. Electron beam must be electrons of the same momentum or velocity and energy.

Light from a LASER beam is monochromatic and coherent. LASER gives the best interference patterns.

The decay of photons give rise to pair production (one electron and one positron). The interaction of matter and antimatter such as electron and positron always produces two photons or more. The production of 2 photons is more probable.

One electron can never turn into a photon by itself. It needs to interact with a positron.

Heisenberg's Uncertainty Principle prohibits the localization of electron hence its path. We know there is a quantum jump between energy levels but we will never know the path exactly. We can find the probability amplitude of the most likely path (the minimum of the difference between potential and kinetic energy of the system's Lagrangian function).